 
Summary: Submitted to the 46th IEEE CDC on 9 Mar 2007
Design of continuoustime flows on intertwined orbit spaces
P.A. Absil C. Lageman J. H. Manton
Abstract Consider a space M endowed with two or more
Lie group actions. Under a certain condition on the orbits of
the Lie group actions, we show how to construct a flow on
M that projects to prescribed flows on the orbit spaces of the
group actions. Hence, in order to design a flow that converges
to the intersection of given orbits, it suffices to design flows on
the various orbit spaces that display convergence to the desired
orbits, and then to lift these flows to M using the proposed
procedure. We illustrate the technique by creating a flow for
principal component analysis. The flow projects to a flow on the
Grassmann manifold that achieves principal subspace analysis
and to a flow on the "shape" manifold that converges to the
set of orthonormal matrices.
I. INTRODUCTION
Given a symmetric positivedefinite n × n matrix A, we
say that a flow on the set Rn×p
of all the n × p real
